Ultrashort optical pulses are produced by mode-locked lasers. Our group is doing research on new ways to mode-lock lasers, specifically fiber lasers. In addition, mode-locked lasers represent a unique system in which to study the propagation of optical pulses. We are also working in this area.
Laser are often divided into two classes, continous wave (cw) and pulsed. However, there are several types of pulsed lasers, the most common being q-switched and mode-locked. Mode-locked lasers produce ultrashort pulses (actually trains of ultrashort pulses) with durations in the picoseconds or femtoseconds whereas q-switched lasers produce pulses on a nanosecond timescale. Mode-locked lasers generate ultrashort pulses by “locking” the phases of many modes such that they constructively interfere to produce a short pulse. Mode-locking requires a device in the cavity that favors short pulses over cw operation, this can either be an active device, such as an acouto-optic modulator, or a passive device, such as a saturable absorber. The shortest pulses are produced by passive mode-locking, typically based on an effective saturable absorber that utilizes the near-instantaneous Kerr effect. The most common example of this is Kerr-lens modelocking of titanium-saphhire (ti:sapphire) lasers.
Mode-locked fiber lasers
While ti:sapphire lasers work very well and can produce the shortest pulses obtained directly from a laser, they have drawback of being bulk optic lasers and requiring relatively expensive pump sources. Laser built based on fiber technology developed for telecommunications have the potential to address these drawbacks. Fiber lasers cannot utilize the Kerr-lens mode-locking used for ti:sapphire lasers because the light is confined in a single transverse mode in single mode-fiber. Instead, the method of nonlinear polarization rotation is typically used, although semiconductor saturable absorbers are also common. Nonlinear polarization rotation also uses the Kerr effect, so it can achieve very short pulses, however it has the disadvantage of depending on the birefringence of the fiber, which arises from built-in and mounting stress and bending of the fiber, and thus is very irreproducible and prone to change over time.
To overcome the disadvantages of non-linear polarization rotation, we have been working on a new approach to mode-locking fibers based on discrete spatial soliton formation in waveguide arrays. This method is analogous to Kerr-lens mode-locking, although it is compatible with fiber lasers. We have demonstrated that can be used to produce a regular pulse train from a fiber laser, although the pulses appear to be “noise bursts” rather than a train of regular pulses (Chao, 2012). We are currently working on developing and improving this approach to mode-locking fiber lasers. This project is a collaboration with Professor Nathan Kutz in the Applied Mathematics Department at the University of Washington.
Pulse propagation effects
A mode-locked laser is a pulsed laser that emits a periodic sequence of optical pulses where the pulses are spaced by the cavity round-trip time (the group delay). These pulses take the form of solitons. In general, the main feature of solitons is that they propagate for a long time without visible changes. Mathematically, a soliton is a localized solution of a partial differential equation describing the evolution of a nonlinear system with an infinite number of degrees of freedom. In dissipative systems, however, the pulse dynamics depend drastically on the system parameters. The evolution can be periodic or chaotic or solitons can be switched from one stable state to another.
For the solitons propagating in mode-locked Ti:sapphire lasers, we have shown that the dominant factor in the pulse dynamics is the equilibrium established between the Kerr nonlinearity and the linear dispersion. The competition between these aspects results in dynamics such as “breathing” of the pulse as it propagates (see figure above). We used an asymptotic theory developed for the perturbed nonlinear Schroedinger equation to predict the dynamics of these solitons using only one fitting parameter in the model to generate the theoretical curves. This study showed that the dispersion management concepts originally developed in fiber communications apply in a much broader context.
In addition, we have measured and modeled nonlinear polarization evolution in microstructure fiber. Comparison between measurement and theory show that chromatic dispersion plays an important role of actually enhancing the nonlinear polarization evolution while decreasing other nonlinearities. In particular, the shape of the final spectrum depends on third-order dispersion.
More recently, in collaboration with Curtis Menyuk of the University of Maryland Baltimore County, we have begun to study the quantum noise properties of mode-locked lasers. In order to be able to predict noise due to amplified spontaneous emission, the fundamental source of noise in all lasers, one has to understand the linear response of the laser. This varies widely from laser to laser and cannot easily be predicted from first principles. So, in order to calculate the noise properties, we had to experimentally characterize a Ti:sapphire laser’s linear response. The results of that will be used to predict the quantum-noise limited linewidth of comb lines, a sort of analogue to the Schawlow-Townes linewidth in cw lasers. This work is described in more detail on our web page about frequency combs.
As part of our work towards developing mode-locked fiber lasers, described above, we have also done measurements on pulse propagation in waveguide arrays, showing that pulse shortening does occur (Hudson, 2008), that the output chirp can be clamped to a fixed value (Hudson, 2012a) and the role of three-photon absorption (Hudson, 2012b).
